During this lengthy period of my life, the greater part of my energy was consecrated to what one might call "piece work": the scrupulous work of shaping, assembling, getting things to work, all that was essential for the construction of all the rooms of the houses, which some interior voice (a demon perhaps? ) exhorted me to build, the voice of a master craftsman whispering to me now and then depending on the way the work was advancing. Absorbed as I was by the tasks of my craft- brick-layer, stone-mason, carpenter, plumber, metal worker, wood worker - I rarely had the time to write down in black and white, save in sketching the barest outlines, the invisible master-plan that except , ( as it became abundantly clear later) to myself underlined everything, and which, over the course of days, months and years guided my hand with the certainty of a somnambulist.(*)
On the basis of what I've been able to see around me at the level of mathematical discovery, these incredible detours of the roads of discovery are characteristic of certain great investigators only. This may be due to the fact that over the last two or three centuries the natural sciences, and mathematics even more so, have gradually liberated themselves from all the religious and metaphysical assumptions of their culture and time. which served as particularly severe brakes on the universal development, ( for better or worse) of a scientific understanding of the universe. It is true, all the same, that some of the most basic and fundamental notions in mathematics (such as spatial translation, the group, the number zero, the techniques of calculus, the designation of coordinates for a point in space, the notion of a set, of a topology, without even going into negative and complex numbers), required millennia for their emergence and acceptance. These may be considered so many eloquent signs of that inherent "block", implanted in the human psyche, against the conceptualization of totally new ideas, even when these ideas possess an almost infantile simplicity, and which one would think would be obvious based on the available evidence, over generations, not to say millennia ....
To return to my own work, I've the impression that the "hand waving" ( perhaps more numerous than those of my colleagues), has been largely over matters of detail. usually quickly rectified by my own careful attention. These might be called simple "accidents of the road" of a purely local character without any serious effects on the validity of the underlying intuitions of the specific situation. On the other hand, at the level of ideas and large-scale intuitions, I feel that my work stands the test of time, as incredible as that may seem. It is this certainty without hesitation of having grasped at every instant, if not exactly the ends to which my thought leads, ( which often enough lie hidden), but at least the most fertile directions which ought to be explored that will lead directly to that which is most essential. It is this quality of "certitude" which has brought to my mind Koestler's image of the "sleepwalker"
In terms of its quantity, my work during these productive years found its concrete expression in more than 12,000 published pages in the form of articles, monographs or seminars(*)
These purely "quantitative" indicators give no more, admittedly, than a crude overview of my work, to the total neglect of those things which gave it life, soul and vigor. As I've written above, the best thing I've brought to mathematics has been in terms of original viewpoints which I've first intuited,then patiently unearthed and developed bit by bit. Like the notions I've mentioned, these original viewpoints, which introduced into a great multiplicity of distinct situations, are themselves almost without limit.
However, some viewpoints are more extensive than others, which along have the capacity to encapsulate a multitude of other partial viewpoints, in a multitude of different particular instances. Such viewpoints may be characterized as "Great Ideas". By virtue of their fecundity, an idea of this kind give birth to a teeming swarm of progeny, of ideas inheriting its fertility, which , for the most part,(if not all of them) do not have as extensive a scope as the mother-concept.
When it comes to presenting a "Great Ideas", to "speak it", one is faced with, almost always, a problem as delicate as its very conception and slow gestation in the person who has conceived it - or, to be more precise, that the sum total laborious work of gestation and formation isthe "expression" of the idea: that work which consists of patiently bringing it to light, day after day, from the mists that surround its birth, to attain, little by little, some tangible form, in a picture that is progressively enriched, confirmed and refined over the course of weeks, months and years. Merely to name the idea in terms of some striking formulation, or by fairly technical key words, may end up being a matter of a few lines, or may extend to several pages. Yet it is very rare to find anyone who, without knowing it in advance, is able to "hear" this "name", or recognize its face. Then, when the idea has attained to its full maturity, one may be able to express it in a hundred or so pages to the full satisfaction of the worker in whom it had its birth . Yet it may also be the case that even a thousand pages, extensively reworked and thought over, will not suffice to capture it.(*)
That piece of my programme on the theme of schemas, their prolongations and their ramifications, that I'd completed at the time of my departure, represents all by itself the greatest work on the foundations of mathematics ever done in the whole history of mathematics(Italics added by the translator so that there should be no misunderstanding of who is speaking), and undoubtedly one of the greatest achievements in the whole history of Science.